The Cyclic Decomposition of cf(Q2q×C10)/ R ̅ (Q29×C10)
DOI:
https://doi.org/10.31642/JoKMC/2018/090104Keywords:
matrix representation, character tables, Quaternion groups, the cyclic decomposition of groupAbstract
In this paper, we propose the cyclic decomposition of the factor group cf(Q2q×C10)‚Z)/R ̅(Q2q×C10 ), and the group cf(Q2q×C10‚Z) is Z-valued class functions of the direct product group ((Q14×C10)) under the operation of addition, and R((Q14×C10)) is the subgroup of the generalized characters of the group cf(Q2q×C10)‚Z).Then cf(Q2q×C10‚Z)/(R() ̅Q2q×C10)) is an abelian factor group denoted by K(Q2q×C10)) where (Q14 is the quaternion group of order28 and C10 is the cyclic group of order 10. Also, we find the rational valued characters table of the group (Q2q×C10 ) when p, and q prime numbers and s∈Z^+ is given as follows : ≡^* (Q2q×C10))=〖 ≡〗^* ((Q14 )⨂≡^* (C10 ) (1) and find the cyclic decomposition of group (Q2q×C10 ) in this paper and prove that K(Q2q×C10 )=⨁_(i=1)^4 [KQ2q ] ⨁_(i=1)^5 K (C10 ) (2)Downloads
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Copyright (c) 2022 Naseer Rasool Albakaa, Habeeb Kareem Al-Bdairi, Neeran Tahir Abd Alameer
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